Multiple choice

How many different words can be formed using the letters of the word AMBIGUOUS, such as all the vowels appear together?

  1. 1,800

  2. 3,600

  3. 6,400

  4. 7,200

  5. None of the above
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D Correct answer
AI explanation

The word AMBIGUOUS has 9 letters with vowels A, I, U, O, U (where U repeats twice) and consonants M, B, G, S. Using the method of bundling, we treat the five vowels as a single unit, making 5 items total (4 consonants and 1 vowel unit). These 5 items can be arranged in 5! ways, and the vowels within the unit can be arranged in 5!/2! ways due to the repeated U. Multiplying these gives 5! * (5!/2!) = 120 * 60 = 7200.

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